Branch structure of J-holomorphic curves near periodic orbits of a contact manifold

dc.creatorHarris, Adam
dc.creatorWysocki, Krzysztof
dc.date2007-01-17
dc.date.accessioned2026-07-07T07:41:42Z
dc.date.available2026-07-07T07:41:42Z
dc.descriptionLet $M$ be a three-dimensional contact manifold and $ψ:D\setminus\{0\}\to M\times{\Bbb R}$ a finite-energy pseudoholomorphic map from a punctured disc in ${\Bbb C}$, that is asymptotic to a periodic orbit of the Reeb vector field. This article examines conditions under which smooth coordinates may be defined in a tubular neighbourhood of the orbit such that $ψ$ resembles a holomorphic curve, invoking comparison with the theory of topological linking of plane complex algebroid curves near a singularity. Examples of this behaviour which are studied in some detail include pseudoholomorphic maps into ${\Bbb E}_{p,q}\times{\Bbb R}$, where ${\Bbb E}_{p,q}$ denotes a rational ellipsoid with contact structure induced by the complex structure of the ambient ${\Bbb C}^{2}$. Contact structures arising from non-standard circle-fibrations of the three-sphere are also examined.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0701496
dc.identifierhttp://arxiv.org/abs/math/0701496
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122210
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.subject32Q65
dc.titleBranch structure of J-holomorphic curves near periodic orbits of a contact manifold
dc.typetext

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